1. Field
Embodiments of the present disclosure relate to calculating position and attitude information associated with a 6-degree-of-freedom stage, and more particularly to calculating position and attitude information associated with a 6-degree-of-freedom stage based on kinematics and displacement and/or movement information received from one or more sensors.
2. Discussion
Importance of ultra-precision position control technology has persistently increased in industries. Particularly, semiconductor technology has been improved due to the demand for higher integration of circuits, such that recent microprocessors have been manufactured including minimum line widths of about 0.18 μm. A stage used to manufacture wafers associated with these microprocessors generally require tolerances of about 1/10 of such line widths and, thereby, typically requiring reproducibility of about 20 nm.
Many technologies may be needed to achieve such small line widths. One important aspect of such technologies is accurate stage control. If stage position control is not accurate, such small widths may not be achieved even when other technologies are applied.
Accordingly, many semiconductor exposure and inspection devices employ a 6-degree-of-freedom stage whose attitude may be accurately and quickly controlled. However, the 6-degree-of-freedom stage may need to float in the air without a guide since each of the degrees of freedom of the stage may need to be controlled. Therefore, it may be difficult to control the position and attitude of the 6-degree-of-freedom stage and it may also be difficult to perform control tuning of the same.
FIG. 1 is a block diagram of a kinematic control system used in association with ultra-precision position control technology.
As shown in FIG. 1, the kinematic control system serves to convert measurement information received from one or more sensors into drive command information that is to be delivered to, for instance, an actuator in order to control the stage so as to have a desired position (coordinates) and/or a desired attitude (angle). Kinematic control systems employing one or more kinematic control techniques may be needed since the measurement position and the drive position of the stage may physically differ.
In this manner, various procedures to obtain solutions to rather complex, burdensome equations may be needed to implement such kinematic control systems. Since such equations associated with 6-degree-of-freedom stages are so complicated, 1) a scheme that uses mathematical simplification or 2) a scheme that uses a plurality of kinematic solutions may be employed for the 6-degree-of-freedom stage.
Both schemes involve an approximation process, which can reduce the accuracy of such kinematic control systems.
Reduction in the accuracy of a kinematic control system greatly affects the accuracy of coordinate parameters, thereby making control tuning difficult. Here, the coordinate parameters indicate coordinates of a valid measurement point of a sensor, coordinates of a mounting position of an actuator, coordinates of a virtual rotation center, and/or the like.
Kinematic control systems that utilize approximation processes may be satisfactorily applied to a certain extent when, for example, rotation angles Tx, Ty, and Tz of the stage are small or negligible. However, as the rotation angle of the stage increases, the rate of error of such approximated kinematic control systems increases proportionally with the rotation angle. Accordingly, such approximated kinematic solutions may not be applied to a stage whose rotational stroke is great.
The above information disclosed in this Background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form any part of the prior art nor what the prior art may suggest to a person of ordinary skill in the art.